- Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
- Vol: 67 Issue: 1
- ZERO-BASED INVARIANT SUBSPACES IN THE BERGMAN SPACE
ZERO-BASED INVARIANT SUBSPACES IN THE BERGMAN SPACE
Authors : Bouabdallah Fatiha, Bendaoud Zohra
Pages : 277-285
Doi:10.1501/Commua1_0000000849
View : 5 | Download : 4
Publication Date : 2018-02-01
Article Type : Research
Abstract :It is known that Beurling’s theorem concerning invariant subspaces is not true in the Bergman space (in contrast to the Hardy space case).However, Aleman, Richter, and Sundberge proved that every cyclic invariantasubspace in the Bergman space Lp(D), 0 < p < +1, is generated by its extremal function. This implies, in particular, that for every zero-based invariantsubspace in the Bergman space the Beurling’s theorem stands true. Here, wecalculate the reproducing kernel of the zero-based invariant subspace Mninathe Bergman space L2(D) where the associated wandering subspace Mnis one-dimensional, and spanned by the unit vector Gn(z) =zMn p n + 1znKeywords : Bergman space, inner function, Beurling’s theorem, kernel function